{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "2DHeatEquation.ipynb",
      "provenance": [],
      "authorship_tag": "ABX9TyOqV+6YBs6BBXx1cFas6y2L",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/Divyanshu-ISM/Oil-and-Gas-data-analysis/blob/master/2DHeatEquation.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "l8A6D8M9V9Rk",
        "colab_type": "text"
      },
      "source": [
        "#2D Simulation : (Heat/Pressure Distribution)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "QtMBxRO0VvCs",
        "colab_type": "text"
      },
      "source": [
        "$\\frac{\\partial U}{\\partial t} = D\\left(\\frac{\\partial^2U}{\\partial x^2} + \\frac{\\partial^2U}{\\partial y^2}\\right)$\n",
        "\n",
        "> This is the governing PDE where  D is the diffusion coefficient\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GiPisuctWZWH",
        "colab_type": "text"
      },
      "source": [
        "##Applying Finite Difference Approximations."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OTJ99FzQWSwm",
        "colab_type": "text"
      },
      "source": [
        "$\\frac{u_{i,j}^{(n+1)} - u_{i,j}^{(n)}}{\\Delta t} = D\\left[ \\frac{u_{i+1,j}^{(n)} - 2u_{i,j}^{(n)} + u_{i-1,j}^{(n)}}{(\\Delta x)^2} + \\frac{u_{i,j+1}^{(n)} - 2u_{i,j}^{(n)} + u_{i,j-1}^{(n)}}{(\\Delta y)^2} \\right],$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wTnJkTFXXwSj",
        "colab_type": "text"
      },
      "source": [
        "$u_{i,j}^{(n+1)} = u_{i,j}^{(n)} + D\\Delta t\\left[ \\frac{u_{i+1,j}^{(n)} - 2u_{i,j}^{(n)} + u_{i-1,j}^{(n)}}{(\\Delta x)^2} + \\frac{u_{i,j+1}^{(n)} - 2u_{i,j}^{(n)} + u_{i,j-1}^{(n)}}{(\\Delta y)^2} \\right]$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VDkfqghgX-Td",
        "colab_type": "text"
      },
      "source": [
        "#Problem Statement:\n",
        "\n",
        "Consider the diffusion equation applied to a metal plate initially at temperature Tcold apart from a disc of a specified size which is at temperature Thot. We suppose that the edges of the plate are held fixed at Tcool. The following code applies the above formula to follow the evolution of the temperature of the plate. It can be shown that the maximum time step, Δt that we can allow without the process becoming unstable is\n",
        "\n",
        "$\\Delta t = \\frac{1}{2D}\\frac{(\\Delta x\\Delta y)^2}{(\\Delta x)^2 + (\\Delta y)^2}$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qyGGGnJwY6dy",
        "colab_type": "text"
      },
      "source": [
        "Approach 1: Loops.(SLOW)\n",
        "\n",
        "##Approach 2: Vectorization (FAST)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wfTADSneVgp2",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt"
      ],
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "FTFxwOc0bU6e",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "outputId": "e3b8c144-5ea4-4df8-fe46-b586f37d386a"
      },
      "source": [
        "plt.figure(figsize=(10,10))\n",
        "plt.style.use('default')"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 720x720 with 0 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XFPliXmIZSu5",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 525
        },
        "outputId": "dd4c4523-afe2-451d-d021-6a866218092b"
      },
      "source": [
        "# plate size, mm\n",
        "w = h = 10.\n",
        "# intervals in x-, y- directions, mm\n",
        "dx = dy = 0.1\n",
        "# Thermal diffusivity of steel, mm2.s-1\n",
        "D = 4.\n",
        "\n",
        "\n",
        "Tcool, Thot = 300, 700\n",
        "\n",
        "nx, ny = int(w/dx), int(h/dy)\n",
        "\n",
        "dx2, dy2 = dx*dx, dy*dy\n",
        "dt = dx2 * dy2 / (2 * D * (dx2 + dy2))\n",
        "\n",
        "u0 = Tcool * np.ones((nx, ny))\n",
        "u = u0.copy()\n",
        "\n",
        "# Initial conditions - ring of inner radius r, width dr centred at (cx,cy) (mm)\n",
        "r, cx, cy = 2, 5, 5\n",
        "r2 = r**2\n",
        "\n",
        "\n",
        "for i in range(nx):\n",
        "    for j in range(ny):\n",
        "        p2 = (i*dx-cx)**2 + (j*dy-cy)**2\n",
        "        if p2 < r2:\n",
        "            u0[i,j] = Thot\n",
        "\n",
        "def do_timestep(u0, u):\n",
        "    # Propagate with forward-difference in time, central-difference in space\n",
        "    u[1:-1, 1:-1] = u0[1:-1, 1:-1] + D * dt * (\n",
        "          (u0[2:, 1:-1] - 2*u0[1:-1, 1:-1] + u0[:-2, 1:-1])/dx2\n",
        "          + (u0[1:-1, 2:] - 2*u0[1:-1, 1:-1] + u0[1:-1, :-2])/dy2 )\n",
        "\n",
        "    u0 = u.copy()\n",
        "    return u0, u\n",
        "\n",
        "# Number of timesteps\n",
        "nsteps = 101\n",
        "# Output 4 figures at these timesteps\n",
        "mfig = [0, 10, 50, 100]\n",
        "fignum = 0\n",
        "fig = plt.figure()\n",
        "for m in range(nsteps):\n",
        "    u0, u = do_timestep(u0, u)\n",
        "    if m in mfig:\n",
        "        fignum += 1\n",
        "        print(m, fignum)\n",
        "        ax = fig.add_subplot(220 + fignum)\n",
        "        im = ax.imshow(u.copy(), cmap=plt.get_cmap('hot'), vmin=Tcool,vmax=Thot)\n",
        "        ax.set_axis_off()\n",
        "        ax.set_title('{:.1f} ms'.format(m*dt*1000))\n",
        "fig.subplots_adjust(right=0.85)\n",
        "cbar_ax = fig.add_axes([0.9, 0.15, 0.03, 0.7])\n",
        "cbar_ax.set_xlabel('$T$ / K', labelpad=20)\n",
        "fig.colorbar(im, cax=cbar_ax)\n",
        "plt.show()"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "0 1\n",
            "10 2\n",
            "50 3\n",
            "100 4\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 640x480 with 5 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OPYvkPJla547",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}